 reserve R for finite Approximation_Space;
 reserve X,Y,Z for Subset of R;
 reserve kap for RIF of R;

theorem Prop6a: :: Proposition 6 a)
  (CMap kap).(X,Y) = 0 iff X c= Y
  proof
    thus (CMap kap).(X,Y) = 0 implies X c= Y
    proof
      assume (CMap kap).(X,Y) = 0; then
      1 - kap.(X,Y) = 0 by CDef;
      hence thesis  by ROUGHIF1:def 7;
    end;
    assume X c= Y; then
A1: kap.(X,Y) = 1 by ROUGHIF1:def 7;
    (CMap kap).(X,Y) = 1 - 1 by A1,CDef;
    hence thesis;
  end;
